P9208 Virtual Person “Nothing”

A phoenix that is not beautiful at all. Those sharp claws are stained with the innocent blood.

You are given a pair sequence $\{(v_i,c_i)\}$ and a rooted tree with root $1$. The weight of node $i$ is $(v_i,c_i)$. - Define the value of a non-root node as the product of all $c$ in its subtree times the product of all $v$ outside its subtree. - Define the value of the root node as the product of all $c$ in its subtree. Formally, if $u$ is not the root, then the value $f_u$ of $u$ is: $$f_u=\prod\limits_{v\in \operatorname{substree}(u)} c_v\times \prod\limits_{v\notin \operatorname{substree}(u)} v_v$$ Otherwise, its value $f_u$ is: $$f_u=\prod\limits_{v=1}^n c_v$$ Find the **sum of the values of all nodes** in the whole tree, and output the answer modulo $m$. Note: **it is guaranteed that $\bm m$ is a prime**.

The first line contains two positive integers $n,m$. The next $n-1$ lines each contain two integers $u,v$, indicating that there is an edge between $u$ and $v$. The next line contains $n$ integers, representing $c_{1, 2, \dots, n}$. The next line contains $n$ integers, representing $v_{1, 2, \dots, n}$.

Output one integer, representing the result of the answer modulo $m$.

### Sample Explanation  (The image is incorrect. The weights $v,c$ should be swapped.) ### Constraints and Notes For $100\%$ of the testdata, $1\le n\leq 3\times 10^5$, $1\leq v_i,c_i,m\leq 10^9$. Translated by ChatGPT 5